Question: Simplify the following expression: $x = \dfrac{y^2 - 3y - 4}{y - 4} $
Answer: First factor the polynomial in the numerator. $ y^2 - 3y - 4 = (y - 4)(y + 1) $ So we can rewrite the expression as: $x = \dfrac{(y - 4)(y + 1)}{y - 4} $ We can divide the numerator and denominator by $(y - 4)$ on condition that $y \neq 4$ Therefore $x = y + 1; y \neq 4$